His drilled shot gave the Bristol club a vital edge to take into the second half.
Not a demonstrative player, Johnson celebrated with a huge leap into the air and his dad Gary - City's manager and former Yeovil boss - was just as excited.
City had been pressing in on Yeovil without finding the final ball, but Johnson's finish was clinical, a cross knocked down to him just outside the box.
City thought they had a second minutes later when centre-back Jamie McCombe bundled the ball in, but referee Mike Dean gave a kick for a foul on goalkeeper Steve Mildenhall.
The home club had another goal disallowed later, a Louis Carey header from a corner.
Johnson senior, drawing on his knowledge of Yeovil used a 4-4-1-1 line-up with limited success.
Yeovil who went into this West Country derby as the leading away scorers in League One were offering hardly a threat, Carey was breaking up their every move while Bradley Orr at right-back was always free to start home raids down the right.
Arron Davies, the liveliest Yeovil runner, tried to signal a change in approach with a sharp right-footed shot as the second period began. Brazilian keeper Adriano Basso did well to cover it at the base of his right post.
But the 3,000 visiting fans in a 19,000 crowd had little to rouse them until sub Andy Lindegaard drew a spectacular save from Basso around the hour.
Overall it was a subdued Yeovil performance and it was all up for them on 70 minutes when Scott Guyett slid into Enoch Showunmi.
He got a red card, City a penalty and Orr pushed that confidently past Mildenhall's right hand to keep City in second place.